Amplitude estimation is a fundamental quantum algorithmic primitive that enables quantum computers to achieve quadratic speedups for a large class of statistical estimation problems, including Monte Carlo methods. The quantum algorithm theorized by QC Ware and Goldman Sachs for Monte Carlo simulations has now been demonstrated in practice on the latest IonQ quantum computer. The teams are designing quantum algorithms intended to let firms evaluate risk and simulate prices for a variety of financial instruments at far greater speeds than today.
“Our research group has been making fundamental contributions to quantum technology. We are working toward enterprise use cases that could have significant impact on strategic investing decisions,” said William Zeng, head of Quantum Research at Goldman Sachs, in a statement. Speeding up speed up Monte Carlo simulations impacts a number of sectors including finance and climate science.
“This is a demonstration of how the combination of insightful algorithms that reduce hardware requirements and more powerful near-term quantum computers has now made it possible to start running Monte Carlo simulations,” said Iordanis Kerenidis, head of Quantum Algorithms – International at QC Ware, in a statement. “While QC Ware has designed novel practical quantum algorithms and software for enterprise implementation, IonQ has built unique hardware with quantum gates of high enough quality to run these algorithms.”
The main drawback from the perspective of near term hardware implementations is that the amplitude estimation algorithm requires very deep quantum circuits. Recent works have succeeded in somewhat reducing the necessary resources for such algorithms, by trading off some of the speedup for lower depth circuits, but high quality qubits are still needed for demonstrating such algorithms.
In a recent paper, researchers from Goldman Sachs, Stanford University, QC Ware and IonQ report the results of an experimental demonstration of amplitude estimation on a state-of-the-art trapped ion quantum computer. The amplitude estimation algorithms were used to estimate the inner product of randomly chosen four-dimensional unit vectors, and were based on the maximum likelihood estimation (MLE) and the Chinese remainder theorem (CRT) techniques.
Significant improvements in accuracy were observed for the MLE based approach when deeper quantum circuits were taken into account, including circuits with more than ninety two-qubit gates and depth sixty, achieving a mean additive estimation error on the order of 10−2. The CRT based approach was found to provide accurate estimates for many of the data points but was less robust against noise on average. Last, they analyzed two more amplitude estimation algorithms that take into account the specifics of the hardware noise to further improve the results.